Aerothermodynamic Analysis of a Blunt Body with Forward

Aerothermodynamic Analysis of a Blunt Body

with Forward Facing Cavity and Opposing Jet

Combination

Mahesh Kavimandan

Cyient Ltd. (Hyderabad)

Bassetti Chandrasheker Cyient Ltd. (Hyderabad)

Abstract— In high-speed travel such as space travel, the heat

produced on the Re-Entry body due to frictional effects is of

major concern. Several studies and research have been done to

overcome this problem with new ideas and theories. This paper

deals with the reduction of aero thermodynamic heating due to

frictional force or drag forces on the surface of the body. In this

paper, various combinations of Forward Facing Cavity are taken

along with opposing Jet stream with different r/d ratio where d

represents the cavity depth and r represents the radius of the

cavity in a blunt body using different pressure and location of the

jet stream. We have analyzed the model at Mach 6.2 i.e.

supersonic condition at 11km of altitude with the help of the CFD

software, Ansys and using its two-module Gambit for meshing

and Fluent for solving. Later, the results are compiled and

compared between a simple blunt body and with various

combinations of the cavity and its depth. The best result is

considered to be the one in which the most heat reduction is

attained.

Keywords—Blunt Body; Forward Facing Cavity; Opposing Jet

I. INTRODUCTION

The research and development of hypersonic vehicles such as

interceptor missiles, hypersonic aircraft, and hypervelocity

projectiles are designed to withstand heat loads at hypersonic

Mach number and strike enemy targets swiftly. As new

spacecraft is designed, the latest traditional measures for

thermal protection such as ablation is tough to satisfy new

designs. For example, let’s consider the reusable requirement.

The combination of high speed and dense atmosphere can

detrimentally increase the aerodynamic heating at the nose

section for such vehicles. The severe heating of the nose

changes the aerodynamics including shape and size, also

damaging the electronic hardware or payload that is contained

inside the nose section. So vehicles should be designed to

withstand such aerothermal loads at the nose cone.

A simple passive design that has been investigated now,

especially for the heat reduction is on missile forward cones by

introducing a forward-facing cavity located at the stagnation

region of a blunt vehicle. It has been established that the

flowfield around a concave nose is similar to the flowfield

around a flat-faced cylinder. Theoretically, a flat-faced cylinder

has minimum stagnation-point heat-transfer rates because of

the radius of the curvature at the nose is infinite, as the heat-

transfer rate is inversely proportional to the square root of the

nose radius.

Cooper measured the heat transfer rates at the stagnation

point of a concave hemispherical nose at Mach numbers of 1.98

and 4.95 [1]. He observed that the steady flow heat-transfer

coefficients were 20 to 50% of the heat-transfer coefficient

associated with the convex nose shape. Hopko and Strauss

investigated on a 30 deg blunted cone with a concave nose

shape indicated that the heating at the stagnation point is

reduced to 1∕8 of the heating for convex noses at Mach number

of 8 [2]. Stallings and Burbank also observed a significant

reduction at the position of stagnation-point heat-transfer rates

for concave hemispherical noses for steady-state flow

conditions compared to convex nose shapes [3]. A sufficiently

deep forward-facing rectangular or cylindrical cavity in

hypersonic flow acts like an organ pipe, and the flow inside the

cavity oscillates at its natural frequency. The oscillation of the

stagnant cavity fluid causes the oscillation of the bow shock

wave, which in turn produces the cooling effect.

A study on the oscillation of bow shock waves and

corresponding heat transfer rates for blunt cones with forward

facing cavity was done at Mach 10 by Sambamurthi et al.

Heubner and Utreja [4]. It was found that for appropriately

deep cavities, the local heat fluxes were reduced on the surface

when the longitudinal pressure oscillations induce large bow

shock oscillations within the cavity. A significant study was

done on the heat flux to a blunt nose projectile armed with nose

cavity at Mach 4.5 by Saravanan et al [5] and Lu and Liu,

Seiler et al. and the results showed that the deepest cavity has

the smallest heat flux [6]. A reduction of 35-40% surface

convective heat transfer rates for a missile-shaped body with a

nose cavity located in the stagnation region at a free-stream

Mach number 8. Lu and Liu proved that deeper the cavity, the

smaller the heat flux, and the mean fluxes increases along the

body surface to reach a peak value near the sharp edge then fall

sharply.

The use of opposing jet from the top of the blunt body

caused a reduction of aerodynamic heating which was

investigated experimentally and numerically. This proved to

be quiet effective at the nose of the blunt body. Hayashi et al

showed the effects of the ratio of stagnation pressure of

opposing jet to free stream on the reduction of aerodynamic

heating [7]. The heat flux decreases at each point of the nose

surface, as the pressure ratio increases. Using the high

precision simulation of Navier Stokes equations, a study on the

influence of free Mach number, jet Mach number, and angle of

attack on the reduction of drag coefficient was done. The

opposing jet through an extended nozzle was proposed by

Tamada et al. [8]. The performance was demonstrated using

CFD analysis. The shape of this device is similar to blowpipes

used by glass blowers. The extended nozzle is intended to

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enlarge the recirculation region even by a weak opposing jet.

No study could be done with opposing jet through an extended

nozzle in high enthalpy hypersonic flow. Naoki Morimoto et

al performed a shock tunnel test campaign which showed the

capability to alleviate aerodynamic heating by the opposing jet

through the extended nozzle [9].

Introduction of lateral jets from the tip of the spike

was by Jiang et al. The lateral jet pushes the conical shock

wave originating from the tip of the spike away from the blunt

body so that it reduces the peak value of pressure and heat flux

around the reattachment point [10]. Experiments were done for

the effects of opposing jets in both stable and unstable

conditions. The results showed the effect of opposing has a

significant decrease in surface heat flux and proved to be

effective on aerodynamic heat reduction around a stagnation

region of a blunt body. Hutt et al experimentally showed that

there is a significant reduction of drag by using a structural

spike extending from the nose of a blunt body flying at a

supersonic speed [11]. Rajesh Yadav et al. have investigated

the aerodynamic heating of a hemisphere–cylinder with a

forward-facing ellipsoid and parabolic cavity at the nose in the

atmosphere. A wide range of ellipsoid and parabolic cavities

of varying depths were used. The simulation results suggest

that the stagnation-point heat flux and the total heat-transfer

rates to the blunt body can be favorably reduced by the

introduction of ellipsoid [12] and parabolic cavities [13].

A. FORWARD FACING CAVITY

Hypersonic vehicles experience high kinetic energy due to its

high speed. This high kinetic energy creates high temperature

which affects the vehicle. This produces a huge loss to the

hypersonic vehicle which leads to damage in a structure,

unwanted change in aerodynamics and also damages the

avionics and payload at the nose of the vehicle. Aerodynamic

heating is one reason which may cause damage to the vehicle.

There are many techniques to reduce aerodynamic heating.

One of the techniques is by using a forward facing cavity.

Forward facing cavity is a cavity made at the front of

the nose of the vehicle. This cavity helps in creating a

recirculation region which plays an important role. It acts like a

cooling effect which reduces the aerodynamic heating. The

flow inside the cavity oscillates at its natural frequency causing

the bow shock wave oscillation which produces a cooling

effect. Many types of research and investigations took place for

the effect of a forward facing cavity. A part of this paper is to

analyze the effects of a forward facing cavity on a blunt body

flying at hypersonic speeds. Previous results proved that deeper

the cavity more is the heat reduction.

Fig. 1: Forward facing cavity

B. OPPOSING JET TECHNIQUE

Another technique to reduce aerodynamic heating is the use of

opposing jet techniques. The total pressure of the opposing jet

is an important parameter. The coolant gases like N2 and He

(inert gases) are used. These are injected which helps in

creating a recirculating region. This recirculating region then

cools down the heating produced at the nose of the vehicle.

Fig. 2: Opposing jet on a blunt body

In this paper, a CFD analysis is done on a blunt body alone, a

blunt body having a forward facing cavity and a blunt body

having a forward facing cavity with an opposing jet. The

combinational thermal protection system reduces much of the

aerodynamic heat which is proved in this paper.

II. CFD ANALYSIS

Computational fluid dynamics (CFD) uses numerical methods

and algorithms to solve and analyze problems involving fluid

flows. The CFD analysis we have used is ANSYS. In this paper,

we have used Gambit for meshing and FLUENT as a solver.

A. PREPROCESSING

This consists of two sections

i. Creation of Geometry

ii. Mesh Generation




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B. GEOMETRY

a) Gambit software is chosen to create geometry and to

mesh it. Firstly, a geometry tool pad is selected and a

baseline is created using line option having a length of

70mm.

b) To create a blunt nose, a curve of radius 20mm is

drawn in front of the baseline and this makes the base

body to the problem statement.

c) A wind tunnel section is created around the base body

with required dimensions, which is the domain of

geometry.

d) Zone assignment i.e. naming the inlet pressure far-

field, outlet pressure far-field, wall and body as

required is done.

e) This step is repeated to create the geometry of various

dimensions, having different r/d ratio for the cavity to

compare results for the problem statement.

f) Similarly, these steps are repeated to create an

opposing jet in the blunt body, with different r/d ratio.

Fig. 3: Geometry of a blunt body

The above geometry is for a blunt body. Its dimensions are

mentioned above. The radius of the nose of the blunt body is

20mm and length is 70mm.

Fig. 4: Blunt Body with Forward Facing Cavity

The above geometry has a cavity of varying depth or r/d ratio.

This paper deals with different r/d ratios 1, 2, 2.5 and different

depths of 4mm, 6mm, 8mm and 10mm.

Fig. 5: Blunt Body with Forward Facing Cavity and Injection

The above geometry is the case of a blunt body having forward

facing cavity and opposing jet. The dimensions are briefly

mentioned in the above figure

L- Overall length of the body (70mm)

D- Base diameter of the body (40mm)

r- Lip radius

d- Depth of the cavity

P- Pressure of the jet stream

The values of r/d were chosen to be 1, 2 and 2.5 and the values

of d were taken to 4, 6, 8,10mm.

C. MESH GENERATION

To generate a mesh in the geometry, edges of the base body

geometry are selected in the mesh tool pad. According to the

First-line method, edge mesh command is later selected to

create nodes on the edge of the geometry. The required face of

the domain geometry is selected to create small elements.

The following pictures are the mesh created for blunt body and

different cases for a blunt body having a forward facing cavity.

Fig. 6: Mesh Generation for a Blunt Body




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Case 2:

After generating geometry for a blunt body with a forward

facing cavity, the ratio of length to diameter is varied from 1,

2 and 2.5 for various depths of cavity ranging from 4, 6, 8 and

10 as shown:

TABLE 1: VARIOUS CASES FOR A BLUNT BODY WITH FORWARD FACING CAVITY

S.No Depth r/d ratio

1 Blunt body -

2 4 1

3 4 2

4 4 2.5

5 6 1

6 6 2

7 6 2.5

8 8 1

9 8 2

10 8 2.5

11 10 1

12 10 2

13 10 2.5

Fig. 7: Mesh Generation for a Blunt Body with 4mm cavity and having r/d

ratio 1

Case 3: In the following case, the blunt body having a forward

facing cavity of 10mm is selected as this shows the best results

for heat reduction. A jet was introduced at three points on the

body

• Tip

• Middle

• Centre of the cavity

The meshed files for these cases are as shown below.

Fig. 8: Mesh Generation for a Blunt Body with 10mm cavity and having jet

introduced at the lip


introduced at middle


introduced at Centre of the cavity

Fig. 11: Mesh Generation for a Blunt Body with 10mm cavity(r/d=2) having

jet introduced at lip

Fig. 12: Mesh Generation for a Blunt Body with 10mm cavity(r/d=2) having

jet introduced at middle

D. QUALITY OF MESH

After the mesh is generated, the quality of the mesh has to be

checked.

• The type of mesh generated is a structured mesh. For

the body and domain, the mesh is a quad structure. In

the case of a cavity, it is a tri primitive structure

• The skewness ratio is 0.4.

• The Growth rate is 0.0001.

E. SOLVER

The next step in CFD analysis is Solver. In this step, all the

boundary conditions and necessary required conditions for the

problem statement are given as inputs in the solver setup. They

are mentioned as follows:




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1. Type: density-based

2. Axis symmetric

3. Energy: on

4. Viscous: Spalart Allmaras

5. Density: ideal gas

6. Property: air

7. Cp: piecewise polynomial

8. Thermal conductivity: kinetic theory

9. Viscosity: Sutherland

10. Flux type: AUSM (advection upstream splitting method)

11. Gradient: green gauss cell-based

12. Flow: second-order upwind

F. BOUNDARY CONDITIONS

1. Operating pressure: 0 pa

2. Absolute pressure: 16066 pa

a. Inlet:

1. Mach no= 6.2

2. Average Temperature = -56.35 Degree Celsius or 216.65K

3. Pressure=16066 N/m2

4. ρ= 0.258 kg/m3

5. 𝜇 = 1.435 × 10−6 ×𝑇1.5

𝑇+110.4= 1.789 × 10−5𝑁

𝑚

𝑠 (1)

6. 𝑅𝑒 = 0.258 × 90 × 10−3 ×1829.012

1.739× 105 = 2442188.53 (2)

7. 𝑎 = √𝛾𝑅𝑇 = √1.4 × 287 × 216.65 = 340.47𝑚/𝑠 (3)

8. Reference area: 0.001256 𝑚2

9. Velocity = 1829.26 m/s

b. Outlet:

1. Temperature: 216.65 K

These boundary conditions are the same and applied for all the

cases of blunt body, blunt body with forward facing cavity and

blunt body with forward facing cavity with opposing jet

combination.

For the case of jet injection, we use pressure injection and we

calculate the injection pressure by using the following terms:

1. 𝑃∞= 16066 Pascal

2. 𝑀= 6.2

3. 𝑃0

𝑃∞= (1 +

𝛾−1∗𝑀∞2

2)

𝛾

𝛾−1 where γ= 1.4 (4)

4. 𝑃0 = 31054683.36

5. 𝑃0𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛

𝑃0∞ = Pressure Ratio (PR) (5)

6. Here the values of PR are taken as 0.025 and 0.05

7. 𝑃0𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛

𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 = (1 +

(𝛾−1)∗𝑀∞2

2)

𝛾

𝛾−1 (6)

8. 𝑇0

𝑇 = (1 +

(𝛾−1)∗𝑀∞2

2) (7)

G. RESULTS AND DISCUSSIONS

a. Blunt Body

The results for the blunt body when exposed to the working

fluid are as shown:

TABLE 2: BLUNT BODY RESULTS

S.No Depth d

(mm)

Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux

(W/m2)

1 Blunt 492.00514 0.90649804 10111.566 -7189401.5

b. Blunt Body with Forward Facing Cavity

Case 1: The results for the blunt body with a forward facing

cavity having r/d=1 are as shown. We can see that the drag

reduces as the depth of the cavity is increased. This is given in

the form of the percentage change in heat transfer and Peak

heat flux when compared to a normal bunt body.

Table 3: Results for r/d=1 for Blunt Body with Forward Facing Cavity

S.No Depth d

(mm)

Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux

(W/m2)

1 4 491.85952

(0.029%)

0.90622974

(0.029%)

-10123.259

(-0.12%)

-4757755

(33.82%)

2 6 490.55664

(0.29%)

0.90382923

(0.29%)

-10183.554

(-0.71%)

-4451855.5

(38%)

3 8 483.73431

(1.64%)

0.89125939

(1.64%)

-9733.4899

(3.45%)

-4093048

(45.90%)

4 10 482.61461

(1.90%)

0.88919639

(1.90%)

-9001.3103

(10.98%)

-3720792

(48.24%)


cavity having r/d=2 are as shown. We can see that the drag

reduces until a certain point and starts to increase beyond that.

The percentage change of heat transfer and peak heat flux

increases on comparing with a normal blunt body.

Table 4: Results for r/d=2 for Blunt Body with Forward Facing Cavity

S.No Depth d

(mm)

Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux

(W/m2)

1 4 488.62653

(0.68%)

0.90027309

(0.68%)

-9926.7171

(1.82%)

-7885392.5

(-9.68%)

2 6 483.23646

(1.78%)

0.89034212

(1.78%)

-9425.091

(6.78%)

-7127353

(0.86%)

3 8 503.44778

(-2.32%)

0.92787611

(-2.32%)

-8739.0962

(13.57%)

-6944527.5

(3.40%)

4 10 546.90089

(-10.56%)

1.0076411

(-10.56%)

-8256.5435

(17.56%)

-6526192.5

(9.76%)


cavity having r/d=2.5 are as shown. The percentage change of

heat transfer and peak heat flux increases on comparing with a

normal blunt body.

Table 5: Results for r/d=2.5 for Blunt Body with Forward Facing Cavity

S.No Depth d

(mm)

Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux

(W/m2)

1 4 488.44079

(0.72%)

0.89993087

(0.72%)

-9787.7987

(3.2%)

-7422774

(-3.24%)

2 6 490.91615

(0.22%)

0.90449161

(0.22%)

-9236.7527

(8.65%)

-7358064

(-2.34%)

3 8 518.68253

(-5.42%)

0.95564997

(5.42%)

-8741.9706

(13.54%)

-6976395.5

(2.96%)

4 10 588.20215

(-20.31%)

1.0837368

(-20.31%)

-8245.0856

(18.81%)

-6738175.5

(7.38%)




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Comparing the above results and plotting in the form of graph.

We get it as shown below.

Graph 1: Total Surface Heat vs Curve Length For r/d=1

From the above graph, we see that the Blunt Body has

maximum heat at the surface which is decreased in 4mm,

6mm, 8mm and 10mm. This shows that as the depth of the

cavity increases the amount of the surface heat flux decreases.

Further, the surface heat becomes constant as we move from

left to right across the geometry.

Graph 2: Static Pressure vs Curve Length for r/d=1

As we move from left to right the static pressure decreases

along the cavity and increases at the lip of the cavity and then

becomes constant along the blunt body. As the depth of the

cavity increases the value of static pressure is less.

Graph 3: Total Surface Heat Flux vs Curve Length for r/d=2

From the above graph as Blunt Body having maximum Heat at

the surface which is decreased in 4mm, 6mm, 8mm and

10mm.This shows that as the depth of the cavity increases the

amount of the surface heat flux decreases. Further, the surface

heat becomes constant as we move from left to right across the

geometry.

Graph 4: Static Pressure vs Curve Length for r/d=2

From the above graph, as we move from left to right the static

pressure decreases along the cavity and increases a little at the

lip of the cavity and then becomes constant along the blunt

body. As the depth of the cavity increases the value of static

pressure is less.

Graph 5: Total Surface Heat Flux vs. Curve Length for r/d=2.5

Blunt Body having maximum Heat at the surface which is

decreased in 4mm, 6mm, 8mm and 10mm.This shows that as

the depth of the cavity increases the amount of the surface heat

flux decreases. The surface heat becomes constant as we move

from left to right across the geometry.

Graph 6: Static Pressure vs Curve Length for r/d=2.5

As we move from left to right the static pressure decreases

along the cavity and increases a little at the lip of the cavity

and then becomes constant along the blunt body. As the depth

of the cavity increases the value of static pressure is less.

c. Best Result From all the above cases, the best results are obtained for a

blunt body with a cavity having a depth of 10mm. So plotting

individually the results for different l/d ratios we get the

following graph.




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Graph 7: Total Surface Heat Flux vs Curve Length for 10mm depth

We can observe that as the value of radius increase from 10 to

25mm there is a reduction in total surface heat flux at the cavity

and goes to approximately the same value along the surface.

Graph 8: Static Pressure vs Curve Length for 10mm depth

From the above graph as we move from 10 to 25mm in radius

the value of static pressure decreases.

H. VARIATION OF CONTOURS

Fig. 13: Variation of Static Temperature across blunt body

From the above figure, we can see that the static temperature

is maximum at the nose and decreases gradually around the

body.

Fig. 14: Variation of Static Pressure across Blunt Body

Here we see that that the static pressure is maximum at the nose

of the body and decreases gradually.

Fig. 15: Variation of Axial Velocity across blunt body

From the figure, we see that the minimum velocity is attained

at the nose of the body due to its high pressure.

Fig. 16: Variation of static pressure across blunt body with 10mm cavity




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Fig. 17: Variation of static temperature across blunt body with 10mm cavity

From the above figure, we can see that the static temperature

decreases gradually around the body due to generation of

circulation region.

Fig. 18: Variation of axial velocity across blunt body with 10mm cavity

From the figure, we see that the minimum velocity is attained

at the nose of the body due to its high pressure.

III. BLUNT BODY WITH FORWARD FACING

CAVITY AND OPPOSING JET

The results for the blunt body with forward facing cavity with

a 10mm cavity turned out to be more productive. Now we

introduce opposing jet at three different locations on the body

and we obtain the results for different pressure ratios as shown:

Table 6: Results for a blunt body with 10mm cavity (r/d=1) with opposing jet

and having pressure ratio 0.05

Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 191.3251107

(29.66%)

0.353038926

(29.66%)

59.76784756

(40.18%)

-7130.461495

(42.40%)

Middle 188.73525

(30.86%)

0.34826004

(30.86%)

57.294601

(42.77%)

-6228.6968

(43.49%)

Cavity 188.2275891

(30.90%)

0.347323287

(30.90%)

52.82919321

(45.74%)

-5959.529479

(45.41%)



Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 188.4701208

(30.89%)

0.347770813

(30.89%)

55.31638583

(40.75%)

-11415.76049

(45.35%)

Middle 1.040361385

(30.28%)

1.040692821

(31.1%)

0.895202045

(43.55%)

1.785755888

(44.51%)

Cavity 212.1696828

(31.56%)

0.391501961

(31.94%)

48.91954804

(46.24%)

-10390.82669

(44.15%)

Table 8: Results for a blunt body with 10mm cavity (r/d=2.5) with opposing

jet and having pressure ratio 0.05

Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat

Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 174.7605163

(31.58%)

0.32247344

(31.56%)

143.9469897

(41.06%)

-2136160.69

(44.92%)

Middle 184.645029

(31.68%)

0.34071265

(31.89%)

136.2362286

(44.12%)

-2025356.374

(44.12%)

Cavity 210.72446

(32.51%)

0.3888352

(32.64%)

127.92724

(47.15%)

-1933057.5

(43.76%)



Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 398.3079614

(14.26%)

0.734969999

(14.26%)

-918.3335574

(40.25%)

-1196337.211

(37.55%)

Middle 392.91629

(15.65%)

0.72502113

(15.65%)

-880.3321

(40.98%)

-1045040.6

(37.45%)

Cavity 391.8594221

(16.15%)

0.723070961

(15.84%)

-811.7210661

(41.15%)

-999880.1454

(36.71%)

Table 10: Results for a blunt body with 10mm cavity (r/d=2) with opposing


Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 392.3643338

(15.15%)

0.724002638

(14.78%)

-849.9368047

(40.72%)

-1915317.694

(37.11%)

Middle 1.040361385

(15.90%)

1.040692821

(15.67%)

0.895202045

(41.58%)

1.785755888

(36.81%)

Cavity 441.7029919

(16.57%)

0.815043822

(16.21%)

-751.6493301

(42.14%)

-1743355.971

(35.18%)

Table 11: Results for a blunt body with 10mm cavity (r/d=2.5) with opposing


Location Drag

(N)

Total Drag

Coefficient

(𝑪d)

Heat Transfer

Rate (W)

Peak Heat

Flux (W/m2)

Tip 378.5022597

(16.76%)

0.698423927

(15.28%)

-345.8186404

(41.58%)

-141752.7771

(36.27%)

Middle 399.9104729

(16.41%)

0.737927027

(16.61%)

-327.2942868

(42.51%)

-134399.9503

(35.91%)

Cavity 456.39419

(17.54%)

0.84215248

(17.64%)

-307.33275

(43.84%)

-128275.12

(34.84%)

The results are now plotted as shown below:

Graph 9: Total Surface Heat Flux vs. Curve Length for 10mm Cavity

As we move from 10 to 25mm in radius the value of heat flux

on tip decreases.




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Graph 10: Total Surface Heat Flux vs. Curve Length for 10,25mm

As we move from PR=0.025 to 0.05 the value of heat flux on

surface decrease as the injection pressure cools the region

around it.

Graph 11: Static Pressure vs. Curve Length for 10,25mm

As we move from PR=0.025 to 0.05 the value of Pressure on

the surface increases.

A. Contours for blunt body with injection at the center

which gives us the best result

Fig. 19: Static Temperature Variation

At the cavity, as the depth increases and the PR increases the

temperature in the cavity decreases and it increases slightly at

the lip and then keeps on decreasing around the body.

Fig. 20: Variation of Axial Velocity

Since there is an increase in the static pressure inside the cavity

the velocity decreases in the cavity and then increases around

the body.

Fig. 21: Variation of Static Pressure

At the cavity, as the depth increases with PR increasing the

static pressure in the cavity increases and it decreases slightly

at the lip and then keeps on decreasing around the body.

IV. CONCLUSION

From the analysis results above, it can be concluded that a

blunt body using forward facing cavity would have more

reduction in aerodynamic heating in the case when the r/d ratio

is more and the length of the cavity is deepest. In this paper,

we have compared the analysis results for different r/d ratio of

1, 2, 2.5 and length of 4mm, 6mm, 8mm and 10mm. It was

found that r/d 2.5 and length 10mm experiences the highest

reduction in aerodynamic heating i.e. the case of a blunt body

having the combinational thermal protection system (forward

facing cavity and opposing jet). The most important and

dependent parameter for this analysis is the pressure ratio (PR)

or mass flow rate. In this paper analysis based on PR varying

from 0.025 to 0.05 for 10 mm having varying r/d 1, 2, and 2.5

is done. It is proved from the results that more the value of PR,

more is the heat reduction for higher r/d ratio i.e. when PR =

0.05 for 10mm length and r/d = 2.5, the heat reduction is almost

41% at the tip, 44% at the middle and 47% at the center.




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REFERENCES

[1] Copper,M., Beckwith, I.E., Jones, J.J. and Gallagher, J.J., 1958. Heat-

transfer measurements on a concave hemispherical nose shape with unsteady-flow effects at Mach numbers of 1.98 and 4.95

[2] Hopko, R.N. and Strass, H.K., 1958. Some Experimental Heating Data

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[3] IBurbank, P.B., 1959. Heat-transfer and Pressure Measurements on a

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[4] Huebner, L.D. and Utreja, L.R., 1987. Experimental flowfield

measurements of a nose cavity configuration (No. 871880). SAE Technical Paper.

[5] Sudarshan, B. and Saravanan, S., 2018. Heat flux characteristics within

and outside a forward facing cavity in a hypersonic flow. Experimental Thermal and Fluid Science, 97, pp.59-69.

[6] Lu, H.B. and Liu, W.Q., 2012. Forward-facing cavity and opposing jet combined thermal protection system. Thermophysics and Aeromechanics, 19(4), pp.561-569.

[7] Hayashi, K., Aso, S. and Tani, Y., 2006. Numerical study on aerodynamic heating reduction by opposing jet. AIAA Journal, 66(1).

[8] Tamada, I., Aso, S. and Tani, Y., 2008, September. Numerical study of the effect of the opposing jet on reduction of aerodynamic heating with

different nose configurations. In 26th International Congress of the Aeronautical Sciences, Anchorage, AL (pp. 14-19).

[9] Morimoto, N., Aso, S. and Tani, Y., 2014. Reduction of aerodynamic

heating and drag with opposing jet through extended nozzle in high enthalpy flow. In Proceedings of the 29th Congress of the International Council of the Aeronautical Sciences, Petersburg, Russia, ICAS.

[10] Han, G. and Jiang, Z., 2018. Hypersonic flow field reconfiguration and drag reduction of blunt body with spikes and sideward jets. International Journal of Aerospace Engineering, 2018.

[11] Hutt, G.R. and Howe, A.J., 1989. Forward facing spike effects on bodies

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[12] Yadav, R. and Guven, U., 2015. Aerodynamic heating of a hypersonic

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vehicle with a forward-facing parabolic cavity at nose. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 228(10), pp.1863-1




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Aerothermodynamic Analysis of a Blunt Body with Forward